基于耦合量子线法和玻色化技术构造拓扑物态的研究

The research on topological matters such as quantum Hall states, topological insulators, topological superconductors, topological semimetal and surface topological order states is one of the hottest topics in contemporary condensed matter physics. Recently, the coupled-wire approach has been shown to be useful tools to construct and describe these topological matters. In this project, we use the coupled-wire approach and bosonization technology to construct and characterize the exotic topological matters such as Weyl superconductor, three-dimensional fractional Weyl semimetal, fractional topological insulators, and novel surface topological order states on surfaces of three-dimensional topological systems. And, then the physical mechanisms and topological quantum behaviors of these topological states are investigated, which can provide physical guidance and theoretical basis for the design of functional topological quantum devices.

量子霍尔态、拓扑绝缘体、拓扑超导体、拓扑半金属和表面拓扑序态等拓扑物质的研究是当今凝聚态物理最热门的课题之一。最近，耦合量子线法已经成为构造和描述这些拓扑物质的有效工具。在本项目中，我们利用耦合量子线法和玻色化技术来构造和表征外尔超导体、三维分数外尔半金属、分数拓扑绝缘体和在拓扑系统表面上新的表面拓扑序态等奇异的拓扑物质。然后，考查这些拓扑物态的物理机理和拓扑量子行为，为功能性拓扑量子器件的设计提供物理指导和理论基础。

本项目以耦合量子线、玻色化技术和密度矩阵重整化群算法为工具，重点研究了构造拓扑强关联量子态和不同物理参数诱导的拓扑量子相变等内容。一方面，我们以超晶格任意子哈伯德模型为例，超晶格势和相互作用会促使系统进入拓扑任意子莫特绝缘体态。更为特殊的是只有任意子统计角的变化时系统实现从超流态进入拓扑任意子莫特绝缘态转变，发生任意子统计诱导的拓扑量子相变。另一方面，以具有空间调制相互作用的无自旋费米子量子线为例，解析和数值证明周期性调制相互作用诱导系统发生拓扑量子相变从金属态进入拓扑电荷密度波态。以相互作用调制因子为横坐标和以准粒子能谱为纵坐标，我们可以发现准粒子能谱具有迷人的分形结构。总之，周期性调制的相互作用可以作为一种调控拓扑量子相变和实现拓扑强关联量子态的新方法。